Pythagoras
Early Life and Education
Pythagoras was born around 570 BC in Samos, an island in the eastern Aegean Sea. His father, Mnesarchus, was a merchant from Tyre. His mother, Pythais, was a native of Samos. He spent his early years in Samos but traveled widely with his father. There are accounts of a young Pythagoras visiting Egypt and learning from the priests of Memphis and Thebes.
Mathematical Discoveries
Pythagoras is perhaps best known for the theorem that bears his name, the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as a^2 + b^2 = c^2, where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
Pythagoreanism
Pythagoras established a philosophical and religious school in Croton (now Crotone, in southern Italy) that had many followers. Pythagoreanism, as his philosophy became known, espoused a number of beliefs and practices, including the immortality and transmigration of the soul, the necessity of personal purity and moral conduct, the harmony of the cosmos and the importance of music and mathematics in understanding it, and the belief in certain symbolic and mystical properties of numbers.
Influence and Legacy
Pythagoras's teachings and beliefs left a significant impact on Plato, and through him, all of Western philosophy. His mathematical contributions, including his famous theorem, have influenced the field of mathematics for over two millennia. Pythagoreanism is considered a precursor to the discovery of mathematical proof, a cornerstone of modern mathematics.